






"""simple docstring"""





def 	lowerCamelCase__			(				_lowerCamelCase			:						str						,							_lowerCamelCase			:						int					) ->							list:
  lowerCamelCase_       	=		word.split()

  def justify(_lowerCamelCase			:						list						,							_lowerCamelCase			:						int						,							_lowerCamelCase			:						int					) -> str:
    lowerCamelCase_       	=		max_width - width
    lowerCamelCase_       	=		len(_lowerCamelCase					)
    if len(_lowerCamelCase					) == 1:
      # if there is only word in line
      # just insert overall_spaces_count for the remainder of line
      return line[0] + " " * overall_spaces_count
    else:
      lowerCamelCase_       	=		words_count - 1
      # num_spaces_between_words_list[i] : tells you to insert
      # num_spaces_between_words_list[i] spaces
      # after word on line[i]
      lowerCamelCase_       	=		spaces_to_insert_between_words * [
          overall_spaces_count // spaces_to_insert_between_words
      ]
      lowerCamelCase_       	=		(
          overall_spaces_count % spaces_to_insert_between_words
      )
      # distribute spaces via round robin to the left words
      for i in range(_lowerCamelCase					):
        num_spaces_between_words_list[i] += 1
      lowerCamelCase_       	=		[]
      for i in range(_lowerCamelCase					):
        # add the word
        aligned_words_list.append(line[i]					)
        # add the spaces to insert
        aligned_words_list.append(num_spaces_between_words_list[i] * ' '					)
      # just add the last word to the sentence
      aligned_words_list.append(line[-1]					)
      # join the aligned words list to form a justified line
      return "".join(_lowerCamelCase					)

  lowerCamelCase_       	=		[]
  lowerCamelCase_       	=		[]
  lowerCamelCase_       	=		0
  for word in words:
    if width + len(_lowerCamelCase					) + len(_lowerCamelCase					) <= max_width:
      # keep adding words until we can fill out max_width
      # width = sum of length of all words (without overall_spaces_count)
      # len(word) = length of current word
      # len(line) = number of overall_spaces_count to insert between words
      line.append(_lowerCamelCase					)
      width += len(_lowerCamelCase					)
    else:
      # justify the line and add it to result
      answer.append(justify(_lowerCamelCase						,							_lowerCamelCase						,							_lowerCamelCase					)					)
      # reset new line and new width
      lowerCamelCase_	,      lowerCamelCase_       	=		[word], len(_lowerCamelCase					)
  lowerCamelCase_       	=		max_width - width - len(_lowerCamelCase					)
  answer.append(' '.join(_lowerCamelCase					) + (remaining_spaces + 1) * ' '					)
  return answer


if __name__ == "__main__":
  from doctest import testmod

  testmod()












"""simple docstring"""





from sympy import diff, lambdify, symbols
from sympy.functions import *  # noqa: F403







def 	lowerCamelCase__			(				_lowerCamelCase			:						str						,							_lowerCamelCase			:						complex						,							_lowerCamelCase			:						str = "x"						,							_lowerCamelCase			:						float = 10**-10						,							_lowerCamelCase			:						int = 1						,							) ->							complex:
  lowerCamelCase_       	=		symbols(_lowerCamelCase					)
  lowerCamelCase_       	=		lambdify(_lowerCamelCase						,							_lowerCamelCase					)
  lowerCamelCase_       	=		lambdify(_lowerCamelCase						,							diff(_lowerCamelCase						,							_lowerCamelCase					)					)

  lowerCamelCase_       	=		starting_point

  while True:
    if diff_function(_lowerCamelCase					) != 0:
      lowerCamelCase_       	=		prev_guess - multiplicity * func(_lowerCamelCase					) / diff_function(
          _lowerCamelCase					)
    else:
      raise ZeroDivisionError('Could not find root'					) from None

    # Precision is checked by comparing the difference of consecutive guesses
    if abs(next_guess - prev_guess					) < precision:
      return next_guess

    lowerCamelCase_       	=		next_guess


# Let's Execute
if __name__ == "__main__":
  # Find root of trigonometric function
  # Find value of pi
  print(F'''The root of sin(x) = 0 is {newton_raphson('sin(x)', 2)}''')

  # Find root of polynomial
  # Find fourth Root of 5
  print(F'''The root of x**4 - 5 = 0 is {newton_raphson('x**4 -5', 0.4 +5j)}''')

  # Find value of e
  print(
      '''The root of log(y) - 1 = 0 is ''',
      F'''{newton_raphson('log(y) - 1', 2, variable='y')}''',
  )

  # Exponential Roots
  print(
      '''The root of exp(x) - 1 = 0 is''',
      F'''{newton_raphson('exp(x) - 1', 10, precision=0.005)}''',
  )

  # Find root of cos(x)
  print(F'''The root of cos(x) = 0 is {newton_raphson('cos(x)', 0)}''')




